基于不定可扩展性概念再探对角线方法

Study on Diagonal Method Based on Indefinite Extensibility Concept

使用对角线方法不仅能得到数理逻辑的基本定理,也能导致逻辑悖论。通过对达米特的不定可扩展性概念及其与对角线方法的关联的考查,指出:(1)西蒙斯没有将不定可扩展性概念与对角线方法关联起来,所以其关于对角线论证不同类型的划分只是表面的;(2)汤姆逊对角线引理并没有刻画出对角线方法的实质;(3)对某概念可以使用对角线方法当且仅当该概念是不定可扩展的;(4)使用对角线方法可以发现不定可扩展性概念,从而为刻画自然语言的动态语义模型提供思路。

Using diagonal method yields not only basic theorems for mathematical logic,but also leads to logical paradoxes.By exa-mining the concept of indefinite extensibility and its association with the diagonal method,this paper points out that:(1)since Simmons does not associate the concept of indefinite extensibility with the diagonal method,its division of“diagonal argument types”is only superficial;(2)Thomson diagonal lemma does not depict the essence of diagonal method;(3)diagonal method can be used for a concept if and only if the concept is indefinite extensibility;(4)the use of diagonal method can help us to find the concept of indefinite extensibility and provide ideas for describing the dynamic semantic model of natural language.